A compound formed by elements `X` and `Y` crystallises in a cubic structure in which the `X` atoms are at the alternate corners of a cube and the `Y` atoms are at the face centres.The formula of the compound is

Options

A. `XY_(3)`
B. `X_(3)Y`
C. XY
D. `XY_(6)`

Explanation

To determine the formula of the compound formed by elements X and Y, we need to analyze the positions of the atoms within the cubic structure as described in the question.

### Step-by-Step Solution:

1. **Understanding the Structure**:
- The question states that X atoms are located at the alternate corners of a cube and Y atoms are at the face centers of the cube.

2. **Counting the X Atoms**:
- In a cube, there are 8 corners. Since the X atoms occupy alternate corners, we will have 4 corners occupied by X atoms.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- Therefore, the total contribution of X atoms in the unit cell is:
\[ \text{Total contribution of X} = 4 \times \frac{1}{8} = \frac{4}{8} = \frac{1}{2} \]

3. **Counting the Y Atoms**:
- There are 6 faces on a cube, and Y atoms occupy the face centers.
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.
- Therefore, the total contribution of Y atoms in the unit cell is:
\[ \text{Total contribution of Y} = 6 \times \frac{1}{2} = 3 \]

4. **Writing the Empirical Formula**:
- From the contributions calculated, we have:
- X: \( \frac{1}{2} \)
- Y: \( 3 \)
- The empirical formula can be written as:
\[ \text{Formula} = X_{\frac{1}{2}}Y_{3} \]

5. **Converting to Whole Numbers**:
- To convert the formula into whole numbers, we multiply the entire formula by 2:
\[ \text{Formula} = X_{1}Y_{6} \]

6. **Final Formula**:
- Thus, the final formula of the compound is:
\[ XY_{6} \]

### Conclusion:
The correct formula of the compound formed by elements X and Y is \( XY_6 \).